### Mathematical Biosciences and Engineering

2019, Issue 1: 474-500. doi: 10.3934/mbe.2019022
Research article

# Modelling and analysis of HFMD with the effects of vaccination, contaminated environments and quarantine in mainland China

• Received: 04 March 2018 Accepted: 13 September 2018 Published: 18 December 2018
• Currently, hand, foot, and mouth disease (HFMD) is widespread in mainland China and seriously endangers the health of infants and young children. Recently in mainland China, preventing the spread of the disease has entailed vaccination, isolation measures, and virus clean-up in the contaminated environment. However, quantifying and evaluating the efficacy of these strategies on HFMD remains challenging, especially because relatively little research analyses the impact of EV71 vaccination for this disease. To assess the effectiveness of these strategies, we propose a new mathematical model that considers vaccination, contaminated environment, and quarantine simultaneously. Unlike the previous studies for HFMD, in which the basic reproduction number $R_{0}$ is the only threshold to decide whether the disease is extinct or not, our results show that another threshold value is needed: $\hat{R}_{0} < 1$ ($R_{0}\leq\hat{R}_{0} < 1$) such that disease is extinct; i.e., the disease-free equilibrium is globally asymptotically stable. Moreover, numerical experiments show that our model may have positive equilibriums even if the basic reproduction number $R_{0}$ is less than 1. In designing a new algorithm based on a BP network to estimate the unknown parameters, this proposed model is put forward to individually fit the HFMD reported cases annually in mainland China from 2015 to 2017. At last, the sensitivity analyses and numerical experiments show that increasing the rate of virus clearance, the vaccinated rate of infants and young children, and the quarantined rate of infectious individuals can effectively control the spread of HFMD in mainland China. Nevertheless, it remains difficult to eliminate the disease. Specifically, our results show that the current vaccine measures starting in 2016 have reduced the total number of patients in 2016 and 2017 by 17% and 22%, respectively.

Citation: Lei Shi, Hongyong Zhao, Daiyong Wu. Modelling and analysis of HFMD with the effects of vaccination, contaminated environments and quarantine in mainland China[J]. Mathematical Biosciences and Engineering, 2019, 16(1): 474-500. doi: 10.3934/mbe.2019022

### Related Papers:

• Currently, hand, foot, and mouth disease (HFMD) is widespread in mainland China and seriously endangers the health of infants and young children. Recently in mainland China, preventing the spread of the disease has entailed vaccination, isolation measures, and virus clean-up in the contaminated environment. However, quantifying and evaluating the efficacy of these strategies on HFMD remains challenging, especially because relatively little research analyses the impact of EV71 vaccination for this disease. To assess the effectiveness of these strategies, we propose a new mathematical model that considers vaccination, contaminated environment, and quarantine simultaneously. Unlike the previous studies for HFMD, in which the basic reproduction number $R_{0}$ is the only threshold to decide whether the disease is extinct or not, our results show that another threshold value is needed: $\hat{R}_{0} < 1$ ($R_{0}\leq\hat{R}_{0} < 1$) such that disease is extinct; i.e., the disease-free equilibrium is globally asymptotically stable. Moreover, numerical experiments show that our model may have positive equilibriums even if the basic reproduction number $R_{0}$ is less than 1. In designing a new algorithm based on a BP network to estimate the unknown parameters, this proposed model is put forward to individually fit the HFMD reported cases annually in mainland China from 2015 to 2017. At last, the sensitivity analyses and numerical experiments show that increasing the rate of virus clearance, the vaccinated rate of infants and young children, and the quarantined rate of infectious individuals can effectively control the spread of HFMD in mainland China. Nevertheless, it remains difficult to eliminate the disease. Specifically, our results show that the current vaccine measures starting in 2016 have reduced the total number of patients in 2016 and 2017 by 17% and 22%, respectively.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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